To find the rate of interest at which $1,087.00 will earn $63.84 in 264 days, we'll use the simple interest formula:

$\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}$

Where:

• $P$ is the principal amount ($1,087.00),
• $R$ is the rate of interest,
• $T$ is the time period in years.

First, we convert the time from days to years:

$T = \frac{264 \text{ days}}{365 \text{ days/year}} \approx 0.7233 \text{ years}$

Now, we rearrange the simple interest formula to solve for $R$:

$R = \frac{\text{SI} \times 100}{P \times T}$

Substituting the values:

$R = \frac{63.84 \times 100}{1087 \times 0.7233}$

Let's calculate this.The rate of interest is approximately 8.12% per annum.

Do you want any further details or have any questions? Here are some related questions you might find useful:

1. How do you calculate compound interest for the same scenario?
2. What is the difference between simple and compound interest?
3. How would the interest change if the time period was 1 year instead of 264 days?
4. What would the interest be if the rate were 10% instead of the calculated rate?
5. How does increasing the principal amount affect the interest earned?
6. What is the formula for continuous compound interest?
7. Can you explain how to calculate the time required to double the investment at the calculated rate?
8. How would taxes affect the interest earned on this amount?

Tip: Always double-check whether the interest is compounded or simple when solving interest rate problems.